As having two previous surgeries myself, I'll tell you what is technically possible and what isn't. For one, many things are possible in rhinoplasty, despite what botched surgery patients want to admit to themselves. Generally speaking, you can take the largest caveman nose you can find and whittle it down to something more modern and symmetrical, and as long as the surgeon does it correctly and by TEXTBOOK standards, there will be NO negative side effects unless the surgeon was drunk during surgery. The honest truth is that rhinoplasty is usually for patients who need a %50 improvement - it's not for the patients who have a Sarah Jessica Parker nose and want to turn it into Natalie Portman's. On a side note, James Franco's nose happens to be very close to the Avatar example you provided, so depending on how close your nose is to to that but worse looking, a smoother nose may be exactly "what the doctor ordered."
HOWEVER, the widening of the bridge is one thing that may be impossible. If you have a thinner bridge, like James Franco, grafts will look extremely unnatural and would have to be placed like a sandwhich (probably has never been done surgically). I'd say again, your options should be to smoothen the tip down if your tip is overbearing, to create a more ethnic look. The Avatar nose is very similiar to the African nose in many aspects, and an African nose may be as far as any surgeon would be willing to take you, if even that far. If you have a more typical aysmettrical overbearing Caucasian nose, the surgeons will only recommend improvement on what you have for a better "you" - not becoming a cartoon character.
As a specialist in the media and social world, I know as well as anyone the profound effect that Avatar has had on people, and there are even subcultures that go as far as being sexually attracted to people who look like the Avatar and just like the "furry", "superhero", "twilight", or "character" subcultures, many of the more obsessed fans dress up as Avatar characters in bed. I'm not poking any fun at this, everyone has their own ideals, but achieving those ideals in a SAFE way is not always possible. Yes, some surgeon who is actually a janitor with no surgical training down in Mexico would perform this, and cause you necrosis and possibly death in the process, just to make a fee. But no surgeon is going to give you a replica of the Avatar nose - it's just not studied, achieved, or follows textbook techniques (for instance, the grafting or widening of the nasal bone is not done.) My advice is to sit back and analyze your wishes, and know that the Avatar subcultere is just a fad and will NOT be around for very long - it would be different if you simply wanted a more soft or feminen nose, as male-to-female, transexual, or "sensitive male" subculture has been around for thousands of years. But Avatar?
My final advice would be to find a Avatar nasal prosthetic and slap that puppy on. I think the nose that you want is a danger road, if your nose isn't close to that goal already.